Normals messed up after applying transform
The problem can also be caused by manifold meshes that have other issues, such as non-uniform normals. I ran into this issue just yesterday. I extruded a single plane into a prism, without realizing that the plane had preexisting issues with its normals. 

As an aside: faces don't actually have normals. Each vert has a normal and a face's normal is calculated from its associated verts. One of my verts must have been upside-down, making the plane's normal... weird. As odd as that is to consider, it can happen.

The tricky part was that the resulting prism looked perfectly fine. The problem manifested in OTHER parts of the same object (as invisible faces), but that were not connected to the prism, even though there was nothing actually wrong with the part of the mesh where the issues manifested. It took me FOREVER to figure out, because I thought it was a non-manifold edge somewhere. Once I recalculated the normals on that prism, (because I'd tried EVERYTHING else) everything was fine.

All of which is to say, the problem may actually be in a part of your mesh that looks totally fine.